
for some constant \(M>0\)  under Hellinger metric \(d\)  as \(n\rightarrow \infty \)  in \(\mathbb {P}_0-\) probability. Note that the conditions on parameters can be held because we assume \(\tau =\operatorname{O}(1)\) , \(\lambda =\operatorname{O}(1)\)  and \(v\)  is some positive constant. Recall that we assumed \(\epsilon _n=o(1)\) . Thus, by Lemma A.1 (ii) in [1]},
\(||\Sigma _0-\Sigma ||_{\operatorname{F}}&\le ||\Sigma _0||_2||\Sigma ||_2||\Omega _0-\Omega ||_{\operatorname{F}}\\&\le \tau ^2 ||\Omega _0-\Omega ||_{\operatorname{F}}\\&\le B\tau ^3 d(p_{\Sigma _0},p_{\Sigma })\) 
